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• W3048654479 abstract "We study the set of connected components of certain unions of affine Deligne-Lusztig varieties arising from the study of Shimura varieties. We determine the set of connected components for basic $s$-conjugacy classes. As an application, we verify the Axioms in cite{HR} for certain PEL type Shimura varieties. We also show that for any nonbasic $s$-conjugacy class in a residually split group, the set of connected components is controlled by the set of straight elements associated to the $s$-conjugacy class, together with the obstruction from the corresponding Levi subgroup. Combined with cite{Zhou}, this allows one to verify in the residually split case, the description of the mod-$p$ isogeny classes on Shimura varieties conjectured by Langland and Rapoport. Along the way, we determine the Picard group of the Witt vector affine Grassmannian of cite{BS} and cite{Zhu} which is of independent interest." @default.
• W3048654479 created "2020-08-18" @default.
• W3048654479 creator A5073235261 @default.
• W3048654479 creator A5087011022 @default.
• W3048654479 date "2020-10-01" @default.
• W3048654479 modified "2023-09-23" @default.
• W3048654479 title "On the connected components of affine Deligne–Lusztig varieties" @default.
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• W3048654479 doi "https://doi.org/10.1215/00127094-2020-0020" @default.
• W3048654479 hasPublicationYear "2020" @default.
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